8.4 Trigonometric Ratios

Background The word trigonometry comes from two Greek terms, trigon (triangle) and metron (measure). A trigonometric ratio is a ratio of the lengths of two sides of a RIGHT triangle. The trig ratios stay constant for any size triangle with the same angle measures.

The Trig Ratios Sine (written as sin θ)- the ratio of the side opposite θ to the hypotenuse. Cosine(cos θ)- the ratio of the side adjacent to θ to the hypotenuse Tangent(tan θ)– the ratio of the side opposite θ to the side adjacent to θ

And to remember this… SOH –CAH – TOA

Example 1 Express each ratio as a fraction and a decimal to the nearest hundredth. A. sin L B. cos L C. tan L D. sin N E. cos N F. tan N

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Example 2 Use a special right triangle to express the cosine of 60˚ as a fraction and a decimal to the nearest hundredth.

Example 3 Find y.

Example 4 Find x.

Inverse Trig Functions sin-1 cos-1 tan-1 These are used whenever you need to get rid of a trig function to find the measure of an angle.

Example 5 Use a calculator to find the measure of angle P to the nearest tenth.

Example 6 Find the measures of the angles.

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